1. The problem statement, all variables and given/known data Consider a vector A = (x^2 - y^2)(i) + xyz(j) - (x + y + z)k and a cube bounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0 and z = 1 Determine the volume integral ∫∇.A dV where V is the volume of the cube Determine the surface integral ∫A.n dS where s is the surface of the cube 2. Relevant equations 3. The attempt at a solution ∇.A = 2x + xz -1 Volume integral = ∫∫∫(all from 0 to 1) (2x + xz -1)dxdydz =1/4 (after simplifying) Surface integral = (all from 0 to 1) ∫∫(x^2-y^2)dydz + ∫∫(x+y+z)dxdy + ∫∫(xyz)dxdz this simplifies to a more complicated term I know that both of these methods must lead to the same answer, so I know that I must be doing something wrong with assigning the integrals to evaluate. Can someone show me how to properly set up the volume and surface integrals? This is what I'm confused about the most.